Evaluating the gapless color-flavor locked phase

In neutral cold quark matter that is sufficiently dense that the strange quark mass Mₛ is unimportant, all nine quarks (three colors; three flavors) pair in a color-flavor locked (CFL) pattern, and all fermionic quasiparticles have a gap. We recently argued that the next phase down in density (as a function of decreasing quark chemical potential μ or increasing strange quark mass Mₛ) is the new ``gapless CFL'' (gCFL) phase in which only seven quasiparticles have a gap, while there are gapless quasiparticles described by two dispersion relations at three momenta. There is a continuous quantum phase transition from CFL to gCFL quark matter at Mₛ²/μ≈2Δ, with Δ the gap parameter. Gapless CFL, like CFL, leaves unbroken a linear combination Q of electric and color charges, but it is a Q conductor with gapless Q-charged quasiparticles and a nonzero electron density. In this paper, we evaluate the gapless CFL phase, in several senses. We present the details underlying our earlier work which showed how this phase arises. We display all nine quasiparticle dispersion relations in full detail. Using a general pairing ansatz that only neglects effects that are known to be small, we perform a comparison of the free energies of the gCFL, CFL, two-flavor (2SC), gapless 2SC, and two-flavor up-strange phases. We conclude that as density drops, making the CFL phase less favored, the gCFL phase is the next spatially uniform quark matter phase to occur. A mixed phase made of colored components would have lower free energy if color were a global symmetry, but in QCD such a mixed phase is penalized severely.